More than 350,000 people turned to food banks for help last year, almost triple the number who received food aid in the previous year and 100,000 more than anticipated, according to the UK's biggest food crisis charity.

The Trussell Trust said the dramatic increase in the use of its food banks was set to continue in the coming months as poorer families struggle financially as a result of the government's welfare reforms.

The Trussell Trust executive chairman, Chris Mould, said: "The sheer volume of people who are turning to food banks because they can't afford food is a wake-up call to the nation that we cannot ignore the hunger on our doorstep."

He added: "Politicians across the political spectrum urgently need to recognise the real extent of UK food poverty and create fresh policies that better address its underlying causes. This is more important than ever as the impact of the biggest reforms to the welfare state since it began start to take effect.

"Since 1 April we have already seen increasing numbers of people in crisis being sent to food banks with nowhere else to go."

Although it has established 345 food banks, the trust says there is insufficient capacity nationally and that between 400 and 650 more food banks are needed to cope with expected demand. It is opening new projects at the rate of three a week, but says geographical gaps in coverage mean "thousands of people are facing hunger today in towns with no food banks".

The rise in the numbers of people using Trussell-Trust-backed food banks in part reflects a 76% increase in the number of food banks set up over the past year. But the trust said it had seen a 170% increase in the number of people given food boxes over the same period.

Nearly a third of food parcel recipients had been referred to the trust because their social security benefits had been delayed. A further 15% came as a result of their benefits being cut or stopped (up from 11% in 2011-12). The trust said the majority of people turning to food banks were working-age families.

Mould said: "We're seeing people from all kinds of backgrounds turning to food banks: working people coming in on their lunch-breaks, mums who are going hungry to feed their children, people whose benefits have been delayed and people who are struggling to find enough work."

Trussell food boxes contain three days' supply of non-perishable foods such as tinned fruit, vegetables, meat and fish as well as pasta, cereal, UHT milk, sauces, tea, and long-life juice. Recipients must be referred by care professionals such as social workers or police officers, and are limited to three vouchers a year.

Mary Creagh, the shadow environment secretary, said: "The UK is the seventh richest country in the world yet we face a growing epidemic of hidden hunger with people increasingly unable to meet their family's basic needs. This incompetent government needs to wake up the human cost of their failed economic policies and change course now."

Although the Trussell figures are one of the most robust indicators of the prevalence of food poverty, they represent just a fraction of the growth in emergency food aid in the UK, much of it small-scale and ad hoc, and run through local churches, community groups and housing associations.

The Salvation Army, which also provides emergency food parcels, said many of its local branches ran informal food banks, but it did not collect statistics on a national basis. Anecdotally, it said several of its local branches – known as "corps" – had witnessed an increase in the number of requests for food parcels.

A spokesman for the Department for Work and Pensions said the rise in numbers of people using food banks was partly explained by the decision of jobcentres to refer some clients to food banks, and partly a reflection of the success of Trussell's own "marketing activity".

He said: "The government already provides a safety net for essentials like food and housing through the benefits system and claimants can also request a benefit advance or help from their local authority where needed."